This answer is about OKB-1 (later known as TsKBEM, then NPO Energia, today known as RSC Energia) spacecrafts.
I plan to edit, to make it more exact and detailed.
Vostok and Voskhod. (3K)
The chief conceptual designer was Konstantin Feoktistov.
The administrative chain of all the people "responsible for the design" looked like that:
- Korolev (OKB-1. Chief designer)
Source, for example: Chertok "Rockets and People", volume 3
Soyuz (7K)
One needs to understand, that the initial designs were the ones of the soviet
lunar programs. Including such complexes as Soyuz A-B-V, for example.
And N1-L3, where L3 = 7K-LOK + LK.
7K-LOK is a kind of Soyuz with the familiar Landing and Orbital modules,
but a larger Service Module. 
The family included such spacecrafts as Soyuz 7K-L1 which were sent to fly around the moon under the names of Zond-5,6,7,8. 
The only structural part all those Soyuz variants have in common is, probably, the landing module. The design works, including the search for the optimal shape, landing schemes, of the Landing Module were headed by Vladimir Timchenko
- Korolev (OKB-1. Chief designer)
- K. Bushuev (Deputy Chief Designer)
- Vladimir Roschin (Head of "Department 11 of Gas Dynamics")
After the concept of the landing module was ready, there was a joint team of Departments 9 and 11 headed by Feoktistov to work out the designs of 7K (i.e. Soyuz).
Good source is the following writeup: Memories of the Soyuz lander module creation (in Russian).
Salyut and Soyuz-T (DOS-7K)
Salyut re-used Almaz hull design, fitted with Soyuz guidance and control systems.
Soyuz-T is a member of Soyuz family adapted to be a ferry serving the station.
The proposal came from a team of TsKBEM engineers (Bushuev, Ohapkin, Chertok, Kryukov, Feoktistov, Raushenbach).
- V. Mishin (Designer General, TsKBEM Head of Enterprise)
- K. Bushuev (Chief Designer, general manager of DOS-7K)
- Yuri Semenov (Lead Designer of DOS-7K complex)
- K. Feoktistov (Deputy Chief Designer, deputy general manager of
DOS-7K)
- Leonid Gorshkov (designer of DOS orbital block)
- P.Tsybin (manager of 7K-T)
- Dmitry Slesarev (Deputy Lead Designer responsible for 7K-T)
Sources of information:
Mir core module (DOS-7) and Zvezda ISS Service Module (DOS-8)
The same RSC Energia '46-49 gives the list of conceptual designers of Mir station, it doesn't go into finer details.
- V. Glushko (Designer General, NPO Energia)
- K.Feoktistov (Deputy Designer General)
- L. Gorshkov (head of department)
- E. Demchenko, A. Nesterenko, M.M.Lemelev, V. Tokarev, F.Arkov, N. Beresnev, V. Bobkov, N. Brukhanov, A. Kochkin and others.
The role of Konstantin Feoktistov
One could note that the only name really belonging to all of the above lists is Konstantin Feoktistov. He has participated in the Sputnik designs. And retired from RSC Energia in 1990, 4 years after Mir launch. In different roles he was creating them all. I am surprised his memoir book is not present on Amazon in English translation.